A cutting tool wears out with a time to failure that is normally distributed. It has a mean of 10 working days and a standard deviation of 2.5 days. Find: The probability of failure before day one The probability of failure after 5 days The days predicted that the tool would survive with a probability of 99

A cutting tool wears out with a time to failure that is normally distributed. It has a mean of 10 working days and a standard deviation of 2.5 days. Find: The probability of failure before day one The probability of failure after 5 days The days predicted that the tool would survive with a probability of 99

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: he lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation…

Q: The amount of coffee in a can has a mean of 350g. The standard deviation is 5g. Use the normal…

A: From the graph we see that between 345 and 355 the probabilities are 0.34 and 0.34 To find the…

Q: The life of a semiconductor laser at a constant power is normally distributed with a mean of…

A: Solution : Given that , mean = = 416 standard deviation = = 136 a) P(x > 516) = 1 - p( x<…

Q: Adult male heights are normally distributed with mean 70.72 inches and a standard deviation of 3.25…

A: According to the given information, we have Adult male heights are normally distributed with, Mean =…

Q: a. Find the probability that sick-leave time of an employee in a month exceeds 120 hours.

A: Normal distribution is also known as the Gaussian distribution . It is a bell shaped , symmetric…

Q: brisk walk at 4 miles per hour, burns an average of 300 calories per hour. If the standard deviation…

A: Given Data Population Mean,μ = 300.0 Population Standard Deviation,σ = 8.0

Q: The life expectancy of a fluorescent tube is normally distributed with a mean of 6,800 hours and a…

A: Let, x: Life expectancy of a fluorescent tube and x~N( μ=6800,σ=1000)

Q: Find the probability that 1 man has weight greater than 160 lb. Assume that weights of males are…

A: Let X represent the random variable Mean=182.9 SD=40.8 X~ Normal (182.9, 40.82)

Q: Mary drives to work each morning, and the trip takes an average of mu = 38 minutes. The distribution…

Q: he average waiting time to be seated for dinner at a popular restaurant is 23.5 minutes, with a…

A: Given: μ=23.5, σ=3.6 The corresponding z-value needed to be computed: The probability that the…

Q: The length of time it takes a group of Senior Citizens to play the one game of Candy Crush computer…

A: Given

Q: A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet…

A: GivenMean(μ)=8.4standard deviation(σ)=1.8sample size(n)=38

Q: Assume that the heights of women are normally distributed with a mean of 64.1 inches and a standard…

A: We have given that. X~N( μ , ?^2 ) μ = 64.1 , ? = 2.3 Z-score =( x - μ )/?

Q: A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally…

A: Given Information : A certain model of automobile has its gas mileage (in miles per gallon, or mpg)…

Q: The average time a person spends shopping in a grocery store is 43 minutes. If the time is normally…

A: Given: The average time a person spends shopping in a grocery store is 43 minutes. The time is…

Q: The speed of fastballs follows a Normal distribution with mean μ = 92 mph and a standard deviation…

Q: A veterinary researcher takes an SRS of 60 horses presenting with colic. The average age of the 60…

A: Given that, μ=10,σ = 8,n= 60 The mean and standard deviation of the sampling distribution of sample…

Q: An expensive watch is powered by a 3-volt lithium battery expected to last five years. Suppose the…

A: The normal distribution is the most useful theoretical distribution for continuous variables. For…

Q: ounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of…

A: (a) Given: μ=25, σ=7 The corresponding z-value needed to be computed: The probability that a…

Q: The average life of a brand of automobile tires is 30,000 miles, with standard deviation of 2,000…

A: Mean = 30000 Standard deviation = 2000

Q: The average gas mileage of a certain model car is 28 miles per gallon. If the gas mileages are…

A: Given,Mean(μ)=28Standard deviation(σ)=1.7

Q: A brisk walk at 4 miles per hour burns an average of 300 calories per hour. If the standard…

A: Given average=μ=300, standard deviation=σ=8

Q: Heights of 2-year-old boys are normally distributed with a mean of 34.2 inches and a standard…

Q: The lifespan of a calculator manufactured by a certain company has a normal distribution with a mean…

Q: The amount of coffee dispensed by a coffee dispensing machine is normally distributed with mean of…

A: Solution

Q: An elevator has a placard stating that the maximum capacity is 4200 lb-28 passengers. So, 28 adult…

A: The random variable weight of male follows normal distribution. The population mean is 181 lb. The…

Q: The average outstanding bill for delinquent customer accounts for a national department store again…

Q: The monthly mean starting salary for clinical officers in rural health facilities is 500,000 UGX…

A: A distribution which is bell shaped and symmetric about the mean, is called normal distribution and…

Q: Suppose that heights of women in Utah are normally distributed with a mean of 74 inches and a…

Q: An elevator has a placard stating that the maximum capacity is 1630 lb—10 passengers. So, 10 adult…

A: Consider that the mean and standard deviation of a random variable X are µ and σ, respectively.…

Q: The amount of coffee in a can has a mean of 350g. The standard deviation is 5g. Use the normal…

Q: The duration of an NBA basketball game during the 2019-20 season is normally dis- tributed with the…

A: Given that, Mean, mu = 152 and standard deviation, s = 12 Z score is given by, z=( 130-152)/12 z=…

Q: An elevator has a placard stating that the maximum capacity is 1860 lb—12 passengers. So, 12 adult…

Q: The average age of managers is 40 years. Assume the variable is normally distributed. If the…

A: Given data,μ=40σ=5P(35<X<46)=?

Q: The heights of 5-year-old children are approximately normally distributed with average height of…

A: Don't use empirical rule here , Use Z- table or Excel(or any other.. ) Use Excel function…

Q: an elevator has a placard stating that the maximum capacity is 4500 Ib-29 passengers. So, 29 adult…

A: a) Given : Population Mean,μ = 177.0 Population Standard Deviation,σ = 39.0 X follows…

Q: The amount of tip the servers in an exclusive restaurant receive per shift is normally distributed…

A: Let X be a random variable representing the amount of tip the servers in an exclusive restaurant…

Q: e average height of mall giraffes is 16.3 feet. If the heights are normally distributed with a…

A: Given data,Mean μ=16.3sd σ=3.2P(15<X<20)=?

Q: The average gas mileage of a certain model car is 27 miles per gallon. If the gas mileages are…

A: The probability that a car has a gas mileage of between 26.8 and 27.3 miles per gallon is obtained…

Q: The average height of flowering cherry trees in a certain nursery is 10.5 feet. If the heights are…

Q: The downtime per day for a certain computing facility has averaged 4.0 hours and a standard…

A: Given that μ=4σ=1.98n=20

Q: a. Determine the probability that the watch's battery will last longer than 3.8 years. b. Calculate…

A: a. The random variable X is defined as the life of the battery which follows normal distribution…

Q: A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into…

A: Let X be the amount of soft drink dispensed in to a cup. Given that X follows normal distribution…

Q: The length of time it takes college students to find a parking spot in the library parking lot…

A: The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the mean…

Q: The life of a Radio Shack record player is normally distributed with a mean of 3.3 years and a…

A: Given, Mean = 3.3 Standard deviation = 0.8 The objective is to find the probability that a…

Q: The number of recorded earthquakes in California in a calendar year is normally distributed with a…

A: Givenmean(μ)=120standard deviation(σ)=15

Q: The duration of an NBA basketball game during the 2019-20 season is normally distributed with the…

A: As per the guidelines we are allowed to solve maximum of 3 sub parts If you need help with other…

Q: The time required to complete a final examination in a particular forestry subject is normally…

A: Solution: Let X be the time required to complete a final examination in a particular forestry…

Q: Children between the ages of 2 and 5 watch an average of 25 hours of television per week. Assume the…

A: Given that, μ=25 hoursσ=3 hoursn=20 The mean and standard deviation of the sampling distribution of…

Question

A cutting tool wears out with a time to failure that is normally distributed. It has a mean of 10 working days and a standard deviation of 2.5 days. Find:

The probability of failure before day one
The probability of failure after 5 days
The days predicted that the tool would survive with a probability of 99%

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution